Topological methods for discontinuous operators and applications

Topological methods are crucial in nonlinear analysis, especially in the study of existence of solutions to diverse boundary value problems. As a well–known fact, continuity is a basic assumption in the classical theory and the clearest limitation of its applicability. That is why most discontinuous...

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Detalles Bibliográficos
Autor: Rodríguez López, Jorge
Tipo de recurso: tesis doctoral
Fecha de publicación:2020
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/20848
Acceso en línea:http://hdl.handle.net/10347/20848
Access Level:acceso abierto
Palabra clave:Materias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120219 Ecuaciones diferenciales ordinarias
Materias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120208 Ecuaciones funcionales
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spelling Topological methods for discontinuous operators and applicationsRodríguez López, JorgeMaterias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120219 Ecuaciones diferenciales ordinariasMaterias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120208 Ecuaciones funcionalesTopological methods are crucial in nonlinear analysis, especially in the study of existence of solutions to diverse boundary value problems. As a well–known fact, continuity is a basic assumption in the classical theory and the clearest limitation of its applicability. That is why most discontinuous differential equations fall outside its scope because the corresponding fixed point operators are not continuous. The main goal of this thesis is to introduce a new definition of topological degree which applies for a wide class of non necessarily continuous operators. This generalization is based on the degree theory for upper semicontinuous multivalued mappings. As a consequence, new fixed point theorems for this class of discontinuous operators are derived. This new theory for discontinuous operators is combined with classical techniques in nonlinear analysis in order to obtain existence, localization and multiplicity results for discontinuous differential equations.Figueroa Sestelo, RubénLópez Pouso, RodrigoUniversidade de Santiago de Compostela. Centro Internacional de Estudos de Doutoramento e Avanzados (CIEDUS)Universidade de Santiago de Compostela. Escola de Doutoramento Internacional en Ciencias e Tecnoloxía20202020-01-0120202020-01-01doctoral thesishttp://purl.org/coar/resource_type/c_db06info:eu-repo/semantics/doctoralThesisapplication/pdfhttp://hdl.handle.net/10347/20848reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostelainstname:Universidad de Santiago de Compostela (USC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:minerva.usc.gal:10347/208482026-06-15T12:47:27Z
dc.title.none.fl_str_mv Topological methods for discontinuous operators and applications
title Topological methods for discontinuous operators and applications
spellingShingle Topological methods for discontinuous operators and applications
Rodríguez López, Jorge
Materias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120219 Ecuaciones diferenciales ordinarias
Materias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120208 Ecuaciones funcionales
title_short Topological methods for discontinuous operators and applications
title_full Topological methods for discontinuous operators and applications
title_fullStr Topological methods for discontinuous operators and applications
title_full_unstemmed Topological methods for discontinuous operators and applications
title_sort Topological methods for discontinuous operators and applications
dc.creator.none.fl_str_mv Rodríguez López, Jorge
author Rodríguez López, Jorge
author_facet Rodríguez López, Jorge
author_role author
dc.contributor.none.fl_str_mv Figueroa Sestelo, Rubén
López Pouso, Rodrigo
Universidade de Santiago de Compostela. Centro Internacional de Estudos de Doutoramento e Avanzados (CIEDUS)
Universidade de Santiago de Compostela. Escola de Doutoramento Internacional en Ciencias e Tecnoloxía
dc.subject.none.fl_str_mv Materias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120219 Ecuaciones diferenciales ordinarias
Materias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120208 Ecuaciones funcionales
topic Materias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120219 Ecuaciones diferenciales ordinarias
Materias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120208 Ecuaciones funcionales
description Topological methods are crucial in nonlinear analysis, especially in the study of existence of solutions to diverse boundary value problems. As a well–known fact, continuity is a basic assumption in the classical theory and the clearest limitation of its applicability. That is why most discontinuous differential equations fall outside its scope because the corresponding fixed point operators are not continuous. The main goal of this thesis is to introduce a new definition of topological degree which applies for a wide class of non necessarily continuous operators. This generalization is based on the degree theory for upper semicontinuous multivalued mappings. As a consequence, new fixed point theorems for this class of discontinuous operators are derived. This new theory for discontinuous operators is combined with classical techniques in nonlinear analysis in order to obtain existence, localization and multiplicity results for discontinuous differential equations.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01
2020
2020-01-01
dc.type.none.fl_str_mv doctoral thesis
http://purl.org/coar/resource_type/c_db06
dc.type.openaire.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
dc.identifier.none.fl_str_mv http://hdl.handle.net/10347/20848
url http://hdl.handle.net/10347/20848
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname:Universidad de Santiago de Compostela (USC)
instname_str Universidad de Santiago de Compostela (USC)
reponame_str Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
collection Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
repository.name.fl_str_mv
repository.mail.fl_str_mv
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